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Two perfect gases (1) and (2) are at tem...

Two perfect gases (1) and (2) are at temperatures `T_(1)` and `T_(2)` . If the number of molecules of the two gases are `n_(1)` and `n_(2)` and the masses of the molecules `m_(1)` and `m_(2)`, find the resulting temperature when the two gases are mixed. Assume that there is no loss of energy on mixing the two gases.

Text Solution

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Total energy of molecules of first gas =`3/2 n_(1)kT_(1)`,
Total energy of molecules of second gas =`3/2 n_(2)kT_(2)`
Let temperature of mixture be `T` then total energy of molecules of mixture =`3/2 k(n_(1) + n_(2))T`
`therefore (3)/(2) (n_(1)+n_(2))kT =3/2 k(n_(1)T_(1) +n_(2)T_(2)) implies T=(n_(1)T_(1) + n_(2)T_(2))/((n_(1)+n_(2)))`
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